I experimented somewhat myself and came up with the build below:
9 supply depot
15 supply depot
@100 gas: factory (=when second barracks finishes)
23 supply depot
(constant scv and marine production)
(stop scv production after you have 20-21 depending on whether you lost scouting scv or not)
30 supply depot
@100% factory: machine shop
@100% academy: stim and 2 medics (should have around 12-14 marines)
@100% machine shop: tank > siege mode
37 supply depot
2 firebats, another tank, resume marine production
marine range @150 gas
You should be sieging his natural around 5:45-6:00 with 1 tank 12-13 marines and 2 medics. You'll have 2 firebats at home and are producing more marines and a second tank. The build includes marine range to finish around 6.30 which is the time mutas would be spawning (at the earliest) in a regular 3 hatch build. It also includes an engineering bay for you to start building turrets at the natural/your own main.
Does anyone have a more effective build order?
An advantages of my build order is that you can sort of on the fly decide to do this build or just proceed with a regular 1 rax FE. It also hits really early if it's a close spawn, you can be at the natural with siege mode ready at 5:45.
Some precautions: This build is vulnerable to a lot of speedlings (and backstabs/interception of reinforcements) and it is quite all-in in nature as you stay on 1 base. You'll need to be scouting with your SCV for as long as possible.
I think this build could be useful for beginners since they often want to do some cheese or 1 base builds to get more familiar with the units, and to limit the amount of necessary macro.